where
we
know
,
find
and
.
Based on the previous observation, will work with the assumption that breaking RSA is equivalent to solving the problem:
Given
where
we
know,
find
and
.
By the same argument we used earlier , to find
or
hence
by division
and
(
we need both to crack RSA), we only have to try all primes less than or equal
to 
.
To find these primes, refering to the text, we will work with the Sieve of Eratosthenes, and block decomposition. The following two observations will be useful.
Given the fact that we know that
and
are less than or equal
to 
,
in order to apply the sieve it suffices mark with primes less than or equal to
.
For the problem at hand, we can make the blocks the same size. Based on the
number of processors, just add an appropriate integer to the greatest integer
in
.
The method:
Find all primes less than or equal to
.
Use 1. and a block decomposition of
,
possibly adjusted to so that the block sizes are the same, to find all primes
less than or equal
to 
.
We only need the primes in 1. to "sieve" each block.
For each prime we only need to begin our "sieving" with
(prime)
Use the blocks of primes computed in 2. (and 1.) to
find
and
.
Diagramatically,
